That's one of my concerns about the Justice League movie. They seem to have Batman getting involved in a lot of witty banter, which does not fit the character at all. It's a good addition to have when it fits, but it's not just something that you can plug into films because it tested well in other films.
It depends on how they do it.
Batman does have a dry sense of humor. Honestly Flash would be better for comic relief, and it sounds like they're pumping up Aqua Man as additional comic relief.
It sounds like they are doing the "I doubt my own humanity" tragic version of Cyborg so the loud and goofy version people know from the cartoons won't be here.
So Flash and Aqua Man can be comic relief, Superman and Wonder Woman can do the "hope-y" thing. Wonder Woman can do substitute comedy in the form of "fish out of water" jokes, while Batman and Cyborg rain on everyone's parade.
In an ideal world, that's how it would work anyway.
As for Green Lantern, that depends entirely on whether they bring Hal Jordan or John Stewart. Hopefully they won't do Hal Jordan after that disaster of a Green Lantern movie. Besides, John makes an
excellent straight man. Marines are inherently good at playing the straight man.